Problem: William is 24 years younger than Vanessa. Vanessa and William first met 3 years ago. Eighteen years ago, Vanessa was 4 times older than William. How old is Vanessa now?
We can use the given information to write down two equations that describe the ages of Vanessa and William. Let Vanessa's current age be $v$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $v = w + 24$ Eighteen years ago, Vanessa was $v - 18$ years old, and William was $w - 18$ years old. The information in the second sentence can be expressed in the following equation: $v - 18 = 4(w - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to solve our first equation for $w$ and substitute it into our second equation. Solving our first equation for $w$ , we get: $w = v - 24$ . Substituting this into our second equation, we get the equation: $v - 18 = 4($ $(v - 24)$ $ -$ $ 18)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $v - 18 = 4v - 168$ Solving for $v$ , we get: $3 v = 150$ $v = 50$.